A piece of ribbon 3700 cm long is cut into 3 parts, A, B and C.
A is 4 times as long as B.
C is 110 cm shorter than B.
Give the answers in cm.
- How much shorter is C than A?
- What is the total length of A and B?
(a)
Choose the shortest length to be 1 u.
Length of C = 1 u
Length of B = 1 u + 110
Length of A = 4 x (1 u + 110) = 4 u + 440
Total length of A, B and C
= 4 u + 440 + 1 u + 110 + 1 u
= 4 u + 1 u + 1 u + 440 + 110
= 6 u + 550
6 u + 550 = 3700
6 u = 3700 - 550
6 u = 3150
1 u = 3150 ÷ 6 = 525
Length of C shorter than A
= 4 u + 440 - 1 u
= 4 u - 1 u + 440
= 3 u + 440
= 3 x 525 + 440
= 1575 + 440
= 2015 cm
(b)
Total length of A and B = 4 u + 440 + 1 u + 110
= 4 u + 1 u + 440 + 110
= 5 x 525 + 550 = 2625 + 550 = 3175 cm Answer(s): (a) 2015 cm; (b) 3175 cm